Abstract
The main purpose of this paper is to examine the distribution of the random amplitude error for the sampling problem in diverse situations, and specific formulas are given, which reveal the connection between the random errors of the sampled values and the amplitude error caused by them. The information loss error is also included as a special case.
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Aldroubi, A., Gröchenig, K.: Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43(4), 585–620 (2001)
Atreas, N., Bagis, N., Karanikas, C.: The information loss error and the jitter error for regular sampling expansions. Sampling Theory in Signal and Image Processing 1(3), 261–276 (2003)
Atreas, N., Benedetto, J.J., Karanikas, C.: Local sampling for regular wavelet and Gabor expansions (to appear)
Benedetto, J.J.: Irregular sampling and frames. In: Chui, C.K. (ed.) Wavelets: A Tutorial in Theory and Applications, pp. 445–507 (1992)
Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Series in Applied Math. SIAM, Philadelphia (1992)
Feichtinger, H., Gröchenig, K.: Error analysis in regular and irregular sampling theory. Appl. Anal. 50, 167–189 (1993)
Gröchenig, K.: Localization of frames, Banach frames, and the invertibility of the frame operator. J. Fourier Anal. Appl. (to appear)
Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, Boston (1998)
Meyer, Y.: Ondelettes Et Opérateurs. Hermann, Paris (1990)
Unser, M.: Sampling–50 years after Shannon. Procdings of the IEE 88(4), 569–587 (2000)
Yang, R.M.: An Introduction to Nonharmonic Analysis. Academic Press, New York
Yang, S.Y.: Local error estimation for samling problems. Appl. Math. Comp. 158, 561–572 (2004)
Yang, S.Y.: Wavelet Frames, Local Sampling Problems and Applications, PhD thesis (2004)
Yang, S.Y., Lin, W.: Local sampling problems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3037, pp. 81–88. Springer, Heidelberg (2004)
Yang, S.Y.: The local property of several operators on sampling. Applicable anal. 83(9), 905–913 (2004)
Yao, K.: Application of reproducing kernel Hilbert spaces–bandlimited signal models. Inform. and control 11, 429–444 (1967)
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Yang, S., Song, Z., Zhou, X. (2006). On the Random Sampling Amplitude Error. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_59
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DOI: https://doi.org/10.1007/11758501_59
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Print ISBN: 978-3-540-34379-0
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